Theorem. (
t22_cqc_the2)
∀k24_qc_lang1 : set → set → set, ∀r2_hidden : set → set → prop, ∀k2_qc_lang1 : set → set, ∀k3_qc_lang1 : set → set, ∀m2_subset_1 : set → set → set → prop, ∀k9_qc_lang1 : set → set, ∀k13_cqc_lang : set → set → set → set, ∀k12_cqc_lang : set → set → set → set, ∀r1_tarski : set → set → prop, ∀v6_ordinal1 : set → prop, ∀v3_ordinal1 : set → prop, ∀v1_ordinal1 : set → prop, ∀v2_ordinal1 : set → prop, ∀v1_xreal_0 : set → prop, ∀v1_xxreal_0 : set → prop, ∀v1_xcmplx_0 : set → prop, ∀k1_xboole_0 : set, ∀esk4_0 : set, ∀esk14_0 : set, ∀esk8_1 : set → set, ∀esk11_0 : set, ∀esk7_0 : set, ∀esk10_0 : set, ∀esk15_0 : set, ∀esk12_0 : set, ∀esk16_0 : set, ∀esk5_0 : set, ∀esk13_0 : set, ∀esk17_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀esk6_0 : set, ∀esk1_0 : set, ∀v7_ordinal1 : set → prop, ∀v5_ordinal1 : set → prop, ∀esk9_2 : set → set → set, ∀k1_zfmisc_1 : set → set, ∀v1_xboole_0 : set → prop, ∀k5_qc_lang2 : set → set → set → set, ∀v2_cqc_the1 : set → set → prop, ∀k8_cqc_lang : set → set → set → set, ∀k2_qc_lang2 : set → set → set → set, ∀m1_subset_1 : set → set → prop, ∀k3_cqc_lang : set → set, ∀m1_qc_lang1 : set → prop, (∀X4 X3 X2 X1, (v2_cqc_the1 (k2_qc_lang2 X1 (k8_cqc_lang X1 X2 (k8_cqc_lang X1 X3 X4)) (k8_cqc_lang X1 (k8_cqc_lang X1 X2 X3) (k8_cqc_lang X1 X2 X4))) X1 → False) → m1_qc_lang1 X1 → m1_subset_1 X4 (k3_cqc_lang X1) → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X4 X3 X2 X1, (v2_cqc_the1 (k2_qc_lang2 X1 (k8_cqc_lang X1 X4 (k8_cqc_lang X1 X3 X2)) (k8_cqc_lang X1 X3 (k8_cqc_lang X1 X4 X2))) X1 → False) → m1_qc_lang1 X1 → m1_subset_1 X4 (k3_cqc_lang X1) → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X4 X3 X2 X1, (v2_cqc_the1 (k2_qc_lang2 X1 (k8_cqc_lang X1 X2 X3) (k8_cqc_lang X1 (k8_cqc_lang X1 X3 X4) (k8_cqc_lang X1 X2 X4))) X1 → False) → m1_qc_lang1 X1 → m1_subset_1 X4 (k3_cqc_lang X1) → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X4 X3 X2 X1, (v2_cqc_the1 (k2_qc_lang2 X1 (k8_cqc_lang X1 X2 X3) (k8_cqc_lang X1 (k8_cqc_lang X1 X4 X2) (k8_cqc_lang X1 X4 X3))) X1 → False) → m1_qc_lang1 X1 → m1_subset_1 X4 (k3_cqc_lang X1) → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X4 X3 X2 X1, (v2_cqc_the1 (k2_qc_lang2 X1 (k8_cqc_lang X1 (k8_cqc_lang X1 X2 X3) X4) (k8_cqc_lang X1 X3 X4)) X1 → False) → m1_qc_lang1 X1 → m1_subset_1 X4 (k3_cqc_lang X1) → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X2 X3 X1, (v2_cqc_the1 (k2_qc_lang2 X1 (k8_cqc_lang X1 X2 (k8_cqc_lang X1 X2 X3)) (k8_cqc_lang X1 X2 X3)) X1 → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X2 X3 X1, (v2_cqc_the1 (k2_qc_lang2 X1 X2 (k8_cqc_lang X1 (k8_cqc_lang X1 X2 X3) X3)) X1 → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X3 X1 X2 X4, (r2_hidden X4 (k24_qc_lang1 X1 X2) → False) → (v2_cqc_the1 (k13_cqc_lang X1 X2 X3) X1 → False) → m1_qc_lang1 X1 → m1_subset_1 X2 (k9_qc_lang1 X1) → v2_cqc_the1 (k13_cqc_lang X1 X2 X4) X1 → m2_subset_1 X4 (k2_qc_lang1 X1) (k3_qc_lang1 X1) → m2_subset_1 X3 (k2_qc_lang1 X1) (k3_qc_lang1 X1) → r2_hidden (k13_cqc_lang X1 X2 X3) (k3_cqc_lang X1) → False) → (∀X4 X2 X3 X1, (r2_hidden X1 (k24_qc_lang1 X2 X3) → False) → m1_qc_lang1 X2 → m1_subset_1 X3 (k9_qc_lang1 X2) → m2_subset_1 X4 (k2_qc_lang1 X2) (k3_qc_lang1 X2) → m2_subset_1 X1 (k2_qc_lang1 X2) (k3_qc_lang1 X2) → r2_hidden X1 (k24_qc_lang1 X2 (k5_qc_lang2 X2 X4 X3)) → False) → (∀X3 X2 X4 X1, (r2_hidden X1 (k24_qc_lang1 X2 X4) → False) → (r2_hidden X1 (k24_qc_lang1 X2 X3) → False) → m1_qc_lang1 X2 → m1_subset_1 X4 (k9_qc_lang1 X2) → m1_subset_1 X3 (k9_qc_lang1 X2) → m2_subset_1 X1 (k2_qc_lang1 X2) (k3_qc_lang1 X2) → r2_hidden X1 (k24_qc_lang1 X2 (k2_qc_lang2 X2 X3 X4)) → False) → (∀X3 X4 X1 X2, X1 = X2 → m1_qc_lang1 X3 → m1_subset_1 X4 (k9_qc_lang1 X3) → m2_subset_1 X2 (k2_qc_lang1 X3) (k3_qc_lang1 X3) → m2_subset_1 X1 (k2_qc_lang1 X3) (k3_qc_lang1 X3) → r2_hidden X1 (k24_qc_lang1 X3 (k5_qc_lang2 X3 X2 X4)) → False) → (∀X3 X2 X4 X1, ((k2_qc_lang2 X1 (k13_cqc_lang X1 X2 X4) (k13_cqc_lang X1 X3 X4)) = (k13_cqc_lang X1 (k2_qc_lang2 X1 X2 X3) X4) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k9_qc_lang1 X1) → m1_subset_1 X2 (k9_qc_lang1 X1) → m2_subset_1 X4 (k2_qc_lang1 X1) (k3_qc_lang1 X1) → False) → (∀X2 X3 X1 X4, (X1 = X4 → False) → (r2_hidden X1 (k24_qc_lang1 X2 (k5_qc_lang2 X2 X4 X3)) → False) → m1_qc_lang1 X2 → m1_subset_1 X3 (k9_qc_lang1 X2) → r2_hidden X1 (k24_qc_lang1 X2 X3) → m2_subset_1 X4 (k2_qc_lang1 X2) (k3_qc_lang1 X2) → m2_subset_1 X1 (k2_qc_lang1 X2) (k3_qc_lang1 X2) → False) → (∀X2 X3 X1, (v2_cqc_the1 (k8_cqc_lang X1 X2 (k12_cqc_lang X1 X3 X2)) X1 → False) → m1_qc_lang1 X1 → m2_subset_1 X3 (k2_qc_lang1 X1) (k3_qc_lang1 X1) → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → False) → (∀X4 X1 X3 X2, (r2_hidden X1 (k24_qc_lang1 X2 (k2_qc_lang2 X2 X3 X4)) → False) → m1_qc_lang1 X2 → m1_subset_1 X4 (k9_qc_lang1 X2) → m1_subset_1 X3 (k9_qc_lang1 X2) → r2_hidden X1 (k24_qc_lang1 X2 X3) → m2_subset_1 X1 (k2_qc_lang1 X2) (k3_qc_lang1 X2) → False) → (∀X4 X1 X3 X2, (r2_hidden X1 (k24_qc_lang1 X2 (k2_qc_lang2 X2 X4 X3)) → False) → m1_qc_lang1 X2 → m1_subset_1 X4 (k9_qc_lang1 X2) → m1_subset_1 X3 (k9_qc_lang1 X2) → r2_hidden X1 (k24_qc_lang1 X2 X3) → m2_subset_1 X1 (k2_qc_lang1 X2) (k3_qc_lang1 X2) → False) → (∀X2 X3 X1, (v2_cqc_the1 (k2_qc_lang2 X1 X2 (k8_cqc_lang X1 X3 X2)) X1 → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X2 X3 X1, ((k13_cqc_lang X1 X3 X2) = X3 → False) → m1_qc_lang1 X1 → m2_subset_1 X3 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X2 (k2_qc_lang1 X1) (k3_qc_lang1 X1) → False) → (∀X2 X3 X1, (m2_subset_1 (k8_cqc_lang X1 X2 X3) (k9_qc_lang1 X1) (k3_cqc_lang X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X2 X3 X1, (m2_subset_1 (k12_cqc_lang X1 X2 X3) (k9_qc_lang1 X1) (k3_cqc_lang X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_qc_lang1 X1) → False) → (∀X2 X3 X1, (m1_subset_1 (k5_qc_lang2 X1 X2 X3) (k9_qc_lang1 X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k9_qc_lang1 X1) → m1_subset_1 X2 (k3_qc_lang1 X1) → False) → (∀X2 X3 X1, (m1_subset_1 (k2_qc_lang2 X1 X2 X3) (k9_qc_lang1 X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k9_qc_lang1 X1) → m1_subset_1 X2 (k9_qc_lang1 X1) → False) → (∀X2 X3 X1, (m1_subset_1 (k13_cqc_lang X1 X2 X3) (k9_qc_lang1 X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_qc_lang1 X1) → m1_subset_1 X2 (k9_qc_lang1 X1) → False) → (∀X2 X3 X1, ((k12_cqc_lang X1 X2 X3) = (k5_qc_lang2 X1 X2 X3) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_qc_lang1 X1) → False) → (∀X2 X3 X1, ((k8_cqc_lang X1 X2 X3) = (k2_qc_lang2 X1 X2 X3) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X2 X1, (v2_cqc_the1 (k2_qc_lang2 X1 X2 X2) X1 → False) → m1_qc_lang1 X1 → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X1 X3 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 X3 X1 → False) → m2_subset_1 X3 X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (m1_subset_1 X1 X3 → False) → m2_subset_1 X1 X2 X3 → m1_subset_1 X3 (k1_zfmisc_1 X2) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m2_subset_1 (esk9_2 X1 X2) X1 X2 → False) → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (m2_subset_1 X1 X3 X2 → False) → m1_subset_1 X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, (m1_subset_1 (k24_qc_lang1 X1 X2) (k1_zfmisc_1 (k3_qc_lang1 X1)) → False) → m1_qc_lang1 X1 → m1_subset_1 X2 (k9_qc_lang1 X1) → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X1, (m1_subset_1 (k3_qc_lang1 X1) (k1_zfmisc_1 (k2_qc_lang1 X1)) → False) → m1_qc_lang1 X1 → False) → (∀X1, (m1_subset_1 (k3_cqc_lang X1) (k1_zfmisc_1 (k9_qc_lang1 X1)) → False) → m1_qc_lang1 X1 → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X1 X2, (v6_ordinal1 X2 → False) → v6_ordinal1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1 X2, (v3_ordinal1 X2 → False) → v3_ordinal1 X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, m1_qc_lang1 X1 → v1_xboole_0 (k3_cqc_lang X1) → False) → (∀X1, m1_qc_lang1 X1 → v1_xboole_0 (k9_qc_lang1 X1) → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_ordinal1 X1 → v2_ordinal1 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v1_xxreal_0 X1 → False) → v1_xreal_0 X1 → False) → (∀X1, (v5_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_xcmplx_0 X1 → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xreal_0 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v2_ordinal1 X1 → False) → v3_ordinal1 X1 → False) → (∀X1, (v1_ordinal1 X1 → False) → v3_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v6_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (v2_cqc_the1 (k8_cqc_lang esk1_0 esk2_0 (k12_cqc_lang esk1_0 esk6_0 esk3_0)) esk1_0 → False) → (r2_hidden esk6_0 (k24_qc_lang1 esk1_0 esk4_0) → False) → (v1_xboole_0 esk17_0 → False) → (v1_xboole_0 esk14_0 → False) → (v1_xboole_0 esk13_0 → False) → ((m2_subset_1 esk6_0 (k2_qc_lang1 esk1_0) (k3_qc_lang1 esk1_0) → False) → False) → ((m2_subset_1 esk5_0 (k2_qc_lang1 esk1_0) (k3_qc_lang1 esk1_0) → False) → False) → ((m2_subset_1 esk3_0 (k9_qc_lang1 esk1_0) (k3_cqc_lang esk1_0) → False) → False) → ((m2_subset_1 esk2_0 (k9_qc_lang1 esk1_0) (k3_cqc_lang esk1_0) → False) → False) → (((k13_cqc_lang esk1_0 esk4_0 esk6_0) = esk3_0 → False) → False) → (((k13_cqc_lang esk1_0 esk4_0 esk5_0) = esk2_0 → False) → False) → (∀X1, (m1_subset_1 (esk8_1 X1) X1 → False) → False) → ((m1_subset_1 esk4_0 (k9_qc_lang1 esk1_0) → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → ((v1_xxreal_0 esk16_0 → False) → False) → ((v1_xcmplx_0 esk16_0 → False) → False) → ((v1_xboole_0 esk16_0 → False) → False) → ((v1_xboole_0 esk11_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v1_xreal_0 esk16_0 → False) → False) → ((v1_xreal_0 esk12_0 → False) → False) → ((v7_ordinal1 esk17_0 → False) → False) → ((v7_ordinal1 esk15_0 → False) → False) → ((v2_ordinal1 esk13_0 → False) → False) → ((v1_ordinal1 esk13_0 → False) → False) → ((v3_ordinal1 esk13_0 → False) → False) → ((v3_ordinal1 esk10_0 → False) → False) → ((m1_qc_lang1 esk7_0 → False) → False) → ((m1_qc_lang1 esk1_0 → False) → False) → False